In this lecture we show that the concepts of controllability and observability are. related to linear systems of algebraic equations. It is well known that a solvable. system of linear algebraic equations has a solution if and only if the rank of the. system matrix is full . Observability and controllability tests will be connected to. the rank tests of ceratin matrices: the controllability and observability matrices.
Here are the standardized sizes in volume for coffee cups and the mug which are used in cafe shops and restaurants (theirs size in different locations can slightly vary). Typically, reflecting common sizes of ceramic and takeaway paper cups, they are: 1  the small cup holds 8 fl oz-fluid ounces.
One US Gal=128 fluid oz...not to be confused with avd oz used in weight, of which 16 make up a pound (not to be confused with the Brittish pound sterling). One cup here is generally 8oz, so one gallon yields 16 cups...unless you mean coffee-cups which usually are 6oz, giving a very odd number of cups per gallon.